On Solvability of One Integral Equation on Half Line with Chebyshev Polynomial Nonlinearity

We consider an integral equation on half-line with Chebyshev polynomial nonlinearity, arising in dynamic theory of universe and p-adic string theory. We prove existence of the positive and monotonically increasing continuous solution in class of essentially bounded functions on half-line. We also found two sided estimates for obtained solution, as well as the limit of solution at infinity (Theorem 2.1). We prove uniqueness of a solution in the certain class of functions (Theorem 2.2). We generalize the results for more general integral equation with "double" nonlinearity (Theorem 2.3). At the end we give some examples of functions, describing nonlinearity. Using suggested constructive solution method, we present some results of numerical calculations, having direct application in cosmology.